I really like all places around the Kii Peninsula (Wakayama/Mie/Nara Prefectures), where you have all sorts of amazing nature, history and food.

You have Koyasan and Kumano Kodo - the latter is a network of trails that connect to the three major holy sites in the peninsula, and there's much more to that. You can easily spend several days in Koyasan, and several days exploring the Kumano Kodo area (even if you opt not for long hikes.) Kumano Nachi Taisha is a particularly scenic place.

Even outside of those two locations there are some amazing places that have rightfully been designated as UNESCO World Heritage sites, including Kimpusen-ji, Yoshimizu Jinja and Yoshino Mikumari Jingu, all in the Yoshino vicinity.

There's also the Ise-Shima area, which is home to some of the best seafood in the country. Particularly (but not limited to) the Ise Spiny Lobster and Abalone.

And if the Mrs. likes pearls, the Mikimoto Pearl Island has a nice exhibit on pearl cultivation as well as a very nice store.

There are other great places South (West?) of Nagoya, including parts of Yamaguchi that are worth checking out, as well as some of the islands on the Seto Inland Sea. But if you have yet to visit the Kii Peninsula, that would be my recommendation. Renting a car is highly recommended.

P.S. - I love Kyushu and Shikoku, so if you expand your geographic range, both islands have some incredible places to visit.